Explore advanced concepts in gravitational physics through this graduate-level lecture from the Warsaw4PhD and GeoPlanet PhD schools. Delve into linearized gravity, symmetries, and Killing vectors before examining energy conservation principles. Investigate the gravitational frequency shift phenomenon and its implications. After a brief intermission, focus on equations of motion in the Newtonian approximation for both massive particles and photons. Analyze the gravitational deflection of light and its application in gravitational lensing. Conclude with an introduction to gravitational waves, laying the groundwork for further study in this cutting-edge field of physics.